Simulation of General Relativistic Shock Waves by a Locally Inertial Godunov Method featuring Dynamical Time Dilation January 10 , 2011
Simulation of General Relativistic Shock Waves by a Locally Inertial Godunov Method featuring Dynamical Time Dilation January 10 , 2011
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采用动态时间膨胀的局部惯性 Godunov 方法模拟广义相对论冲击波 2011 年 1 月 10 日
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发表时间：
2011
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通讯作者：
B. Temple
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作者：
Zeke V ogler;B. Temple
我们介绍了我们所谓的局部惯性Goddom方法与动力学时间膨胀，并证明其收敛于一个新的一个参数家庭的球对称，广义相对论冲击波解的爱因斯坦方程的完美流体。这里介绍的前向时间模拟解决了Smoller-Temple冲击波模型[10]中的二次反射波（入射冲击波），用于爆炸进入静态奇异等温球。后向时间的解决方案表明黑洞的形成从一个光滑的解决方案，通过崩溃与传入的稀疏波。数值方法的一个新特点是在每个网格单元中动态扩张时钟，以模拟时空曲率的影响。初始数据集是通过在标准史瓦西坐标系中将弗里德曼-罗伯逊-步行者时空与托尔曼-奥本海默-阿斯托夫时空在一个Lipschitz连续点上匹配，从而产生一个冲击波相互作用点来构建的。据我们所知，这是第一次在广义相对论中数值模拟激波相互作用。Groah和Temple先前的工作证明了满足初始数据的爱因斯坦约束方程仅在度量的Lipshitz连续性的弱水平上。
We introduce what we call the locally inertial Godunov method with dynamical time dilation, and demonstrate its convergence on a new one parameter family of spherically symmetric, general relativistic shock wave solutions of the Einstein equations for a perfect fluid. The forward time simulations, presented here, resolve the secondary reflected wave (an incoming shock wave) in the Smoller-Temple shock wave model [10] for an explosion into a static singular isothermal sphere. The backward time solutions indicate black hole formation from a smooth solution via collapse associated with an incoming rarefaction wave. A new feature of the numerical method is that clocks are dynamically dilated in each grid cell to simulate the effects of spacetime curvature. The initial data set is constructed by matching a Friedmann-Robertson-Walker spacetime to a Tolman-Oppenheimer-Volkoff spacetime in Standard Schwarzschild Coordinates at a point of Lipschitz continuity, creating a point of shock wave interaction. As far as we know, this is the first numerical simulation of shock wave interaction in general relativity. Prior work of Groah and Temple justifies meeting the Einstein constraint equations for the initial data only at the weak level of Lipshitz continuity in the metric.